Digital Signal Processing - Classification of Discrete Time Signals

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Just like Continuous time signals, Discrete time signals can be classified according to the conditions or operations on the signals.

Even and Odd Signals

Even Signal

A signal is said to be even or symmetric if it satisfies the following condition;

Here, we can see that x(-1) = x(1), x(-2) = x(2) and x(-n) = x(n). Thus, it is an even signal.

Odd Signal

A signal is said to be odd if it satisfies the following condition;

From the figure, we can see that x(1) = -x(-1), x(2) = -x(2) and x(n) = -x(-n). Hence, it is an odd as well as anti-symmetric signal.

Periodic and Non-Periodic Signals

A discrete time signal is periodic if and only if, it satisfies the following condition −

Here, x(n) signal repeats itself after N period. This can be best understood by considering a cosine signal −

x (n + N) = A cos (2 π f 0 (n + N) + θ) = A cos (2 π f 0 n + 2 π f 0 N + θ)

For the signal to become periodic, following condition should be satisfied;

x (n + N) = x (n)

i.e.

2 π f_{0} N

is an integral multiple of

2 π

2 π f 0 N = 2 π K

\Rightarrow N = K f 0

Frequencies of discrete sinusoidal signals are separated by integral multiple of

2 π

Energy and Power Signals

Energy Signal

Energy of a discrete time signal is denoted as E. Mathematically, it can be written as;

If each individual values of

x (n)

are squared and added, we get the energy signal. Here

x (n)

is the energy signal and its energy is finite over time i.e

0 < E < \infty

0 < E < \infty

Power Signal

Average power of a discrete signal is represented as P. Mathematically, this can be written as;

Here, power is finite i.e. 0<P<∞. However, there are some signals, which belong to neither energy nor power type signal.

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Robert Karamagi

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Calculus III - 3-Dimensional Space: Equations of Lines